Power Attack and Statistics

[Stalker0]

To put this in a less mathematical, and more situational approach, I went ahead and crunched some numbers using the melee combat calculater. (Note: I don't know who created it, but I really wish I could give them some praise b/c its an awesome program)

First I assumed a lvl 11 Fighter (3 attacks) with a 16 str, weapon focus, weapon spec, improved crit, with a masterwork battleaxe (weilded one-handed). Assume a monster with set AC's, no miss chance, and no DR. And then determined the optimum power attack for max avg damage.

For AC 10: PA-8
AC 15: PA-4
AC 18: PA-2
AC 20: PA-1
AC 22: PA- 0
AC 30: PA- 0.

Now assuming that fighter had a +3 battleaxe.
AC 10: PA-9
AC 15: PA-5
AC 18: PA-2
AC 20: PA-1
AC 22: PA-0
AC 30: PA-0
AC 38: PA-11 (once the AC is to the point that only 20 dice rolls can hit, then of course power attack for max).

Fighter with a +5 battleaxe.
AC 10: PA-9
AC 15: PA-7
AC 18: PA-4
AC 20: PA-2
AC 22: PA-0
AC 30: PA-0

*Remember that a beter strength mod and a lower enchantment equal the same results. A fighter with a 20 strength and a +1 battleaxe would yield the same results as table 2.

Now instead of a battleaxe, we'll try a longsword (effect of crits on this setting)

Masterwork longsword:
AC 10: PA-8
AC 15: PA-4
AC 18: PA-2
AC 20: PA-1
AC 22: PA-0
AC 30: PA-0

Flaming Longsword (I know this can never happen, just bear with me)
AC 10: PA-8
AC 15: PA-3
AC 18: PA-1
AC 20: PA-0
AC 22: PA-0
AC 30: PA-0

Longsword +3:
AC 10: PA-9
AC 15: PA-5
AC 18: PA-2
AC 20: PA-1
AC 22: PA-0
AC 30: PA-0

Keen Longsword +3:
AC 10: PA-9
AC 15: PA-5
AC 18: PA-2
AC 20: PA-1
AC 22: PA-0
AC 30: PA-0

Longsword +5:
AC 10: PA-9
AC 15: PA-7
AC 18: PA-4
AC 20: PA-2
AC 22: PA-0
AC 30: PA-0

After all this data was compiled I came to the following conclusions:
1) AC is the predominat factor on when to power attack
2) Crit range has absolutely no bearing on how much to power attack.
3) Your enhancement bonus due to weapons or strength has only a minor effect on how much to power attack and only in the AC 15-18 region.
4) Additional weapon damage on the weapon (flaming, shocking, etc) has a noticable effect on power attack (it lowers the PA you should use). THe more of such extra damages, the less you should power attack.
5) Having a AC of 10 really sucks


Just a reminder that this only determines these effects on power attack, not on overall damage done.

If I have some time later I'll post results on using two weapons, or a weapon in two hands.

 

[Staffan]

Celebrim, I think you give crits too much credit. The chance to crit gives 'normal weapons' (those with 20/x3 or 19-20/x2 crit types) exactly 10% extra damage assuming that a hit is made and all damage is multiplied and that all threats are hits. (Those with 20/x2 give 5% and those with 20/x4 or 18-20/x2 give 15%.)

It's 10% anyway you slice it - the chance of rolling 19-20 followed by a hit is exactly one tenth of the chance of rolling any hit (including 19-20), and leads to a 100% increase in damage. 100%*10% = 10%. The only times where a crit rating of 19-20/x2 does not lead to a 10% increase in average damage are:

1. Opponents immune to criticals (undead, oozes, constructs, etc.)
2. A 19 won't hit (in which case you can treat it as a 20/x2 weapon instead).
3. Some of the damage won't be increased by crits (sneak attack, elemental dice)
   [/list=1]
   One might think that item 2 would make weapons with high crit multipliers better than weapons with high threat ratings, but the problem rarely comes up - at least unless you go nuts and start getting keen scimitars with improved critical. Also, there's a greater chance of "overkill" with high crit multipliers - if you're fighting a 5 hp hobgoblin, does it really matter whether you'll hit him for 2d10+4 or 3d10+6 (bastard sword vs. waraxe)?
   
   Paradoxically, Power Attack is at its best when used against opponents with either very low AC or very high AC. Very low AC has been demonstrated in the thread already. Versus opponents with ACs so high you're already missing on anything but natural 20s, you don't have anything to lose so you might as well hit them with everything you have.
   
   All things taken together, Power Attack rarely does increase damage all that much. On the other hand, it *is* at the bottom of that particular feat tree, and gives access to Cleave which is pretty good.

 

[trentonjoe]

WOW! YOu guys are good. I am going to have to reread this a ton of times to have it all make sense.

 

[Crothian]

Okay, we have a lot of good inforamtion but you are all going on the assumption that you know what the AC you're trying to hit is. I did a poll on that a few days back and few people seem to know the AC ahead of time. Poll:

http://enworld.cyberstreet.com/showthread.php?s=&threadid=20260

 

[Grommilus]

Statistically, power attack is better the less amount of damage you deal. If you swing around a 20 pound great axe, with a phat strength like 22, you deal 15.5 points of damage per hit. Now, assuming you get 3 attacks a round, power attack becomes attractive when their ac is the same as your bonus to hit (requiring a 0 to hit, makes sense with irritative attacks). Power attacking for one point yeilds a 1.6 percent damage point increase, (34.65 as compared to a 34.1). Not considering criticals, too much work =).
If you have a pansy dagger and a strength of 14, dealing 4.5 points of damage per hit, power attacking becomes attractive at 7 to hit, if you power attack one point, its 5.775, compared to 5.4 points of damage. In perspective, at 0 to hit, Power attacking for 5 yeilds 15.75 damage, compared to no power attack being 12.1, a 30 percent increase in damage.

Therefore, power attack is the feat to take for finese fighters, if you can get 13 str =). Now the feats after power attack, such as cleave and sunder, are big 2 hander fighter feats. If you use a big weapon, the extra attack from cleave will do more damage, and if you have grand cleave, that extra attack has a better chance of dropping your target and getting a second cleave attempt.

Also, one of the best uses of power attack is the destruction of immobile objects, like doors and sleeping dragons =) (had a character that caried a scythe for the sole purpose of power attack coup de grace against sleeping foes, especially the ones with mean fort saves).

Grom

 

[Grommilus]

to trentonjoe, my guess is ac 21 is the ac to power attack one point, and then every 1 or 2 ac lower add another power attack. I have a calculation based on my barbarian at 12th level, but it's dependant on damage and I haven't bothered formulating it.

Btw, Cheiromancer, that equation is wack. 47/4? weight number of attacks by 5/4? don't know where you got it, but don't consider it again =)

Grom

 

[Cheiromancer]

Btw, Cheiromancer, that equation is wack. 47/4? weight number of attacks by 5/4? don't know where you got it, but don't consider it again =)

Grom

It is a fairly insane formula, but when n=1 it is equivalent to Petrosian's method.

But I don't know how it was derived, so I'm not going to commit to it.

 

[Jens]

Cheiromancer had this formula from somewhere:

P = (47-5N-2D)/4 -T/2
Where N is the number of attacks, D is the average damage per attack, and T is the target number (the number you need to hit your opponent's AC).

Initially I got it to 'almost' fit my rule of thumb above. The 'almost' was due to silly mistake pointed out by Meds below.

Here's how the two come out the same (corrected):

My rule of thumb: use PA so that D = AS (where AS is the average number of sides on d20 which will score a hit) which means I should choose P so that

D+P = AS-P or in otherwords choose P = (AS-D)/2

The average number of sides depends on average target number: AS = 21-AT

The average target number depends on the target number of the primary attack and the number of attacks: AT = T-2.5*(N-1)

Substituting those into the formula for P above, one gets Cheiromancer's formula. Which by the way is reasonably easy to use because the whole first term can be calculated beforehand. Inserting attack bonus +21/+16/+11 and damage d8+14 (average 18.5) it becomes

Full attack: P = (47-5*3-2*18.5)/4 -T/2 = -1.25 -T/2
Single attack: P = (47-5*1-2*18.5)/4 -T/2 = 1.25 -T/2

The problem here is with the domain. The formula only works when no attack always hit or miss except on a 1 or 20. In other words, T must be at least 2 and no more than 19-5*(N-1) so the domain for T becomes: [2 , 24-5N]. The result for the character above is that he should not PA where the formula holds. (The closest is P = 0.25 when taking a single attack against AC 23.)

 

[Meds]

Am I doing something wrong since I get 42 instead of 47?

I think the difference arises here:

The average target number depends on the target number of the primary attack and the number of attacks: AT = T-2.5*N

I think that the correct formula for AT is:
AT = T-2.5*(N-1)
(Consider the trivial case of N=1), and for monks that's:
AT = T-1.5*(N-1)

The additional 2.5 gives you the 47 you want, instead of 42.

 

[KarinsDad]

Dwarven Fighter 9/Bard3
BAB:+11
Attack Bonus with Battle Axe: +21/+16/+11
(11BAB+6 STR+3magic weapon+1 Weapon Focus)
Damage:1-8 +14 (19/x3)

Some of the math above is extremely suspect. I will attempt to simplify this for you (with a lot of examples, just go to the bottom of the post to get the bottom line).

There are basically two cases here, full round attack and single attack. So, for each of these cases, we look for when your average damage = average to hit (including criticals).

Full Round Attack:

AC 22 is the break even point where one point of Power Attack helps.

AC 22 = 95% hit + 75% hit + 50% hit or 220% chance to hit = 220% damage or 2.2 * (18.5) * 1.2 = 48.84.

If you add one for Power Attack here, you would get:

AC 22 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (19.5) * 1.2 = 49.140.

But, if you add two for Power Attack here, you would get:

AC 22 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (20.5) * 1.2 = 47.97.

So, adding one point at AC 22 helps, adding 2 points hurts (ever so slightly).

Anything AC 23 or higher can only be hurt by Power Attack.

AC 23 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (18.5) * 1.2 = 46.62.

If you add one for Power Attack here, you would get:

AC 23 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (19.5) * 1.2 = 45.63.

Basically, once you decrease all 3 chances to hit by 5% (in this case), you are doing more harm than adding slightly less than a 5% increase to 3 sets of damage.


Now, the other side of the coin here is to figure out how much Power Attack to add to ACs lower than 22. The answer for this case is real simple. Every 2 points of AC below 22 should have one more added to Power Attack since you are increasing the overall to hit by 20% while increasing the damage by almost 15% (5% times 3 attacks, at least for the higher ACs).

So, a nice rule of thumb for this character is:

(23 - AC) / 2 round up = points to add to Power Attack OR
(24 - AC) / 2 round down, depending on your preference

To illustrate this, let’s take an AC of 10.

AC 10 = 95% hit + 95% hit + 95% hit or 285% chance to hit = 285% damage or 2.85 * (18.5) * 1.2 = 63.27.

If you add 7 for Power Attack here (as per the rule of thumb), you would get:

AC 10 = 95% hit + 95% hit + 75% hit or 265% chance to hit = 265% damage or 2.65 * (25.5) * 1.2 = 81.09.

If you add 6 for Power Attack here, you would get:

AC 10 = 95% hit + 95% hit + 80% hit or 270% chance to hit = 270% damage or 2.7 * (24.5) * 1.2 = 79.38.

If you add 8 for Power Attack here, you would get:

AC 10 = 95% hit + 90% hit + 70% hit or 255% chance to hit = 255% damage or 2.55 * (26.5) * 1.2 = 81.09.

So, this is one of those weird cases where adding 7 to power attack is the same as adding 8 to power attack. Adding 9 to power attack will, yet again, decrease the average damage.

In any case, for the ACs that your character will encounter, the full round rule of thumb above is accurate enough to give you really good information as to what to add once you figure out your opponents AC.

Whew!!!


Single Attack:

AC 23 is also the point at which it does not help to add for a single attack.

AC 23 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.

If you add one for Power Attack here, you would get:

AC 23 = 90% chance to hit = 90% damage or 0.90 * (19.5) * 1.2 = 21.06.

The equation is similar to full round attack:

23 - AC = points to add to Power Attack


AC 22 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.

If you add one for Power Attack here, you would get:

AC 22 = 95% chance to hit = 95% damage or 0.95 * (19.5) * 1.2 = 22.23.

If you add two for Power Attack here, you would get:

AC 22 = 90% chance to hit = 90% damage or 0.90 * (20.5) * 1.2 = 22.14.

Taking an AC 12 example since 11 is the most you can add to Power Attack:

AC 12 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.

If you add 11 for Power Attack here (the maximum), you would get:

AC 12 = 95% chance to hit = 95% damage or 0.95 * (29.5) * 1.2 = 33.63.

If you add 10 for Power Attack here, you would get:

AC 12 = 95% chance to hit = 95% damage or 0.95 * (28.5) * 1.2 = 32.49.

If you add 12 for Power Attack here (if it were allowed), you would get:

AC 12 = 90% chance to hit = 90% damage or 0.9 * (30.5) * 1.2 = 32.94.


So, the answer for this specific character is:

Full Round Attack:

(23 - AC) / 2 round up = points to add to Power Attack OR
(24 - AC) / 2 round down, depending on your preference

Single Attack:

23 - AC = points to add to Power Attack

One other note on this: Criticals are totally irrelevant to the conversation. As you can see above, it does not matter what percentage a critical increases your average damage. Power Attack does not change that percentage. What matters is the "to hit" to "damage" ratio and getting those two numbers as close as possible. A square 4x4 has 16 square units. A square 3x5 has 15 square units. The closer you get a rectangle to a square (by adding a unit to the smaller side and subtracting it from the larger side), the more square units you get. Ditto for this. It's the same type of math.